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How is the Rational Root Theorem expressed in mathematical notation?
I have come up with my own but I'm not sure of it at all
{P(x) | an ... a0 (is an element of) Z}
↓
{x = p/q | p = (factors of a0); q = (factors of an)}
I'm new to this and I hope you guys could help me and explain what it means as well. Thank you very much
1 Answer
- ?Lv 63 years ago
That's pretty close. Using as much notation as possible, a comma to indicate "and" in the list of assumptions, and (p,q)=1 for GCD(p,q), I have:
( P(x) ε Z[x], deg(P) = n, P(p/q) = 0, p,q ε Z, (p,q)=1 )
iff
p|a_0, q|a_n
You need to include the fact that p/q is in lowest terms.
